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CONTENTS xiii
Chapter X

EXISTENCE THEOREMS ....................264

1. The method of successive approximations. 2. Implicit functions. 3. The rank
theorem. 4. Differential equations. 5. Comparison of solutions of differential
equations. 6. Linear differential equations. 7. Dependence of the solution on
parameters. 8. Dependence of the solution on initial conditions. 9. The theorem
of Frobenius.

Chapter XI

ELEMENTARY SPECTRAL THEORY................312

1. Spectrum of a continuous operator. 2. Compact operators. 3. The theory of
F. Riesz. 4. Spectrum of a compact operator. 5. Compact operators in Hilbert
spaces. 6. The Fredholm integral equation. 7. The Sturm-Liouville problem.

Appendix

ELEMENTS OF LINEAR ALGEBRA.................358

1. Vector spaces. 2. Linear mappings. 3. Direct sums of subspaces. 4. Bases.
Dimension and codimension. 5. Matrices. 6. Multilinear mappings. Determi-
nants. 7. Minors of a determinant.

References.............................380

Index...............................381



	CONTENTS xiii Chapter X EXISTENCE THEOREMS ....................264 1. The method of successive approximations. 2. Implicit functions. 3. The rank theorem. 4. Differential equations. 5. Comparison of solutions of differential equations. 6. Linear differential equations. 7. Dependence of the solution on parameters. 8. Dependence of the solution on initial conditions. 9. The theorem of Frobenius. Chapter XI ELEMENTARY SPECTRAL THEORY................312 1. Spectrum of a continuous operator. 2. Compact operators. 3. The theory of F. Riesz. 4. Spectrum of a compact operator. 5. Compact operators in Hilbert spaces. 6. The Fredholm integral equation. 7. The Sturm-Liouville problem. Appendix ELEMENTS OF LINEAR ALGEBRA.................358 1. Vector spaces. 2. Linear mappings. 3. Direct sums of subspaces. 4. Bases. Dimension and codimension. 5. Matrices. 6. Multilinear mappings. Determi- nants. 7. Minors of a determinant. References.............................380 Index...............................381